Second Harmonic Generation Induced byLongitudinal Components in Indium Gallium

Phosphide Nanowaveguides

Nicolas Poulvellarie,1,2,∗ Utsav Dave,3 Koen Alexander,2 Charles Ciret,4Fabrice Raineri,5 Sylvain Combrie,6 Alfredo De Rossi,6 Gunther Roelkens,2

Simon-Pierre Gorza,1, Bart Kuyken,2 and Francois Leo1

1 OPERA-Photonique, Universite libre de Bruxelles, Brussels, Belgium2 Photonics Research Group, Ghent University-IMEC, Ghent, Belgium

3 Department of Electrical Engineering, Columbia University, New York, USA4Laboratoire de Photonique d’Angers EA 4464, Universite d’Angers , Angers, France5 Laboratoire de Photonique et de Nanostructures, CNRS-UPR20, Marcoussis, France

6 Thales Research and Technology, Palaiseau, France∗ Email: Nicolas.Poulvellarie@ulb.ac.be

Abstract: We experimentally demonstrate second harmonic generation in Indium GalliumPhosphide waveguides by mixing transverse and longitudinal components of the optical fields.We confirm the excitation of an antisymmetric second harmonic mode through modal imaging.OCIS codes: (130.3120) Integrated optics devices; (190.4223) Nonlinear wave mixing

1. Introduction

Integrated photonic circuits are revolutionizing nonlinear optics as they allow for strong confinement in materials withelevated nonlinear indices. While third order nonlinear interaction have been the most studied by far, novel integratedplatforms such as lithium niobate [1] or III-V semiconductors on-insulator [2] are renewing interest in second-ordernonlinear processes such as second harmonic generation. III-V seminconductors promise record conversion efficien-cies as they are characterized by very large second-order nonlinear coefficients (one order of magnitude larger thanLiNbO3). However, only a single independent tensor element is nonzero (χ(2)

xyz and permutations). Previous demon-strations of second harmonic generation used waveguides that are rotated by 45° with respect to the crystallographicaxes in order to split the main transverse component along two directions [2, 3]. Conversely, we show here that thestrong longitudinal component of the pump mode can be leveraged to efficiently generate a second harmonic wave ina waveguide aligned with a crystal axis.

2. Theory

We consider a pump optical mode and its second harmonic, ~E(~r, t) = ℜ{a(z)~ea(x,y)ei(βaz−ω0t) +b(z)~eb(x,y)ei(βbz−2ω0t)}, propagating in a III-V nanowaveguide along the z direction. ~ea,b(x,y) are the spatialdistributions of the electric field in the transverse plane, normalized such that the field amplitudes a,b are expressed in√

W. In the case of negligible propagation loss and pump depletion, the second harmonic power along the waveguideis |b(z)|2 = |κ|2|a(0)|4z2sinc2(∆βL/2) where ∆β = 2βa−βb and κ is the effective nonlinearity. When the propagationdirection is aligned with a crystallographic axis, it reads:

κ =ω0ε0

2

∫χ(2)xyz(e∗xb ey

aeza + e∗yb ex

aeza + e∗zb ex

aeya)

dA. (1)

Importantly the effective nonlinearity would vanish in this case for purely transverse modes. But in high index contrastwaveguides, optical modes are known to display large longitudinal components. We compute the modes of a 680 nmwide, 320 nm thick Indium Gallium Phosphide nanowaveguide. Our simulations predict phase matching between aquasi transverse fundamental pump mode around 1575 nm and a higher order second harmonic mode The effectiveindices as well as the different electric field component are shown in Fig. 1(a). We readily note the field componentsof a same mode have very different spatial distributions. Moreover, most have non-negligible amplitudes, confirmingthe need for full vectorial modeling in order to predict nonlinear coupling in III-V nanowaveguides. We compute aneffective nonlinearity κ = 75(

√Wm)−1, corresponding to a conversion efficiency of 50%/(Wcm2).

(a)

Fig. 1. (a) Simulation of the effective indices of a pump mode (black) and a SH mode (green).The spatial distribution of the different electric field components is shown as inset. (b-c) Measuredand computed spatial distribution of the intensity of the SH at the output of the waveguide. (d-e)Measured and computed spatial distribution of the intensity of a 775 nm TM fundamental wave forcomparison. The field of view for theoretical modes is 1.5 µm x 1 µm. (f) Second harmonic powercollected at the output of the waveguide as a function of the pump wavelength.

3. Experimental results

To confirm these theoretical predictions, we fabricated 1.5 mm long InGaP waveguides. We follow the process de-scribed in [4] but we rotate the epitaxial stack by 45° before bonding it to the silicon-on-insulator wafer. This isbecause the cleave directions for III-V semiconductors grown on (100) substrate are [110] and [110]. Following therotation, waveguide facets cleaved along the silicon [011] direction are aligned with a crystallographic axis of theindium Gallium Phosphide layer. We launch a 3 mW telecom band pump in the waveguide through a lensed fiberand collect the second harmonic by use of a high NA (0.9) objective. The sinc2-shaped transmission around 775 nmis shown in Fig. 1(c). From the experiment, we estimate a maximum experimental conversion of 0.2 %/W/cm2 withpump at 1572 nm, in good agreement with the computed phase mathing wavelength. The experimental efficiency how-ever is around 2 orders of magnitude less than the theoretical prediction. This is likely due to strong propagation lossesat the second harmonic but could also be because of low collection efficiency or waveguide inhomogeneities. Furtherexperimental investigations are ongoing to shed light on this discrepancy. Next we imaged the second harmonic modein a microscope arrangement with a nominal magnification of 416. We find good agreement with the theoretical Poynt-ing vector intensity [Fig. 1(c)], confirming the excitation of the predicted antisymetric higher order mode. To calibrateour imaging system, we injected 775 nm light through the lensed fiber to excite a fundamental mode around the SHwavelength [See Fig. 1(d),(e)].

4. Conclusion

We experimentally observed second harmonic generation through mixing of transverse and longitudinal field compo-nents in an Indium Gallium Phosphide nanowire. Not only does it demonstrate the vector nature of the propagatingwaves, it also allows to excite higher order modes with different symmetries.

References

1. C. Wang, et al., ”Ultrahigh-efficiency wavelength conversion in nanophotonic periodically poled lithium niobatewaveguides”, Optica, 5, 1438 (2018).

2. L. Chang, et al., ”Heterogeneously Integrated GaAs Waveguides on Insulator for Efficient Frequency Conver-sion”, Laser & Photonics Reviews 12, 1800149 (2018).

3. D. Duchesne, et al., ”Second harmonic generation in AlGaAs photonic wires using low power continuous wavelight”, Opt. Express 19, 12408 (2011).

4. U. Dave, ”Nonlinear properties of dispersion engineered InGaP photonic wire waveguides in the telecommuni-cation wavelength range”, et al., Opt. Express 23, 4650 (2015).